Finite Group Databasebeta

← #15879539

Subgroups — #15879539

Order 3328.

1110 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719244C211yesmaximal, characteristic
2C2×#11718489C211yesmaximal, characteristic, complemented
3#13117748C211yesmaximal, characteristic, complemented
4#13115804C211yesmaximal, characteristic, complemented
5#13115803C211yesmaximal, characteristic, complemented
6#13115795C211yesmaximal, characteristic, complemented
7#13115792C211yesmaximal, characteristic, complemented
8#13115791C211yesmaximal, characteristic, complemented
9#13115782C211yesmaximal, characteristic, complemented
10#13114834C211yesmaximal, characteristic
11#13114834C211yesmaximal, characteristic
12#13114663C211yesmaximal, characteristic
13#13114661C211yesmaximal, characteristic
14#102×Dic13C211yesmaximal, characteristic
15C13×#1802C211yesmaximal, characteristic
16C2×C4×D4×C13C2211yescharacteristic
17C2×D4×Dic13C2211yescharacteristic
18C2×D4×Dic13C2211yescharacteristic
19C2×#88178—21no—
20C22×#6101—21no—
21#11719244—24no—
22#11719244C418yescomplemented
23C2×#88144C2211yescharacteristic
24C2×#88142C2211yescharacteristic
25C2×#88141—21no—
26C2×#88132—21no—
27C2×#88132—21no—
28C2×#88124C2211yescharacteristic
29C2×C4×Dic26C2211yescharacteristic
30C2×C13×C4⋊C8C2211yescharacteristic
31C2×C13×#102C2211yescharacteristic
32C2×C13×#102C2211yescharacteristic
33C13×#384C2211yescharacteristic
34C2×#88072C2211yescharacteristic
35C2×#88072C2211yescharacteristic
36C2×#88055C2211yescharacteristic
37C2×#88054C2211yescharacteristic
38C2×#88054C2211yescharacteristic
39C2×C8×Dic13C2211yescharacteristic
40#11718637C2211yescharacteristic
41#11718637C2211yescharacteristic
42C4⋊C4×Dic13C2211yescharacteristic
43C4⋊C4×Dic13C2211yescharacteristic
44#11718634—21no—
45#11718633—21no—
46#11718633—21no—
47C4×C4⋊Dic13C2211yescharacteristic
48C2×#88043C2211yescharacteristic
49#11718489—24no—
50C13×#340C2211yescharacteristic
51C13×#340C2211yescharacteristic
52#11718143C2211yescharacteristic
53#11718143C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718143C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718121C2211yescharacteristic
61#11718121C2211yescharacteristic
62C22×D4×C13C2311yescharacteristic
63C23×C4×C13—21no—
64C23×Dic13—21no—
65C23×Dic13—21no—
66C22×Dic26—21no—
67C22×Dic26D411yescharacteristic
68C22×C8×C13C2311yescharacteristic
69C22×C8×C13C2311yescharacteristic
70C4×D4×C13—22no—
71C4×D4×C13C2×C414yes—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C13×C4⋊C4C2311yescharacteristic
77C2×C13×C22⋊C4—21no—
78C2×C42×C13C2311yescharacteristic
79C2×C22⋊Dic13—21no—
80C2×C22⋊Dic13—21no—
81D4×Dic13—22no—
82D4×Dic13—22no—
83D4×Dic13C2×C414yes—
84D4×Dic13C2×C414yes—
85C2×C4⋊Dic13—21no—
86C2×C4⋊Dic13D411yescharacteristic
87C2×C4⋊Dic13C2311yescharacteristic
88C2×C4⋊Dic13C2311yescharacteristic
89C2×C4⋊Dic13C2311yescharacteristic
90C2×C4⋊Dic13C2311yescharacteristic
91#88178—28no—
92C2×#6101—21no—
93C2×#6101—21no—
94C2×#6101—21no—
95C2×#6101—21no—
96C2×#6101—28no—
97C2×#6101—21no—
98C2×#6101—21no—
99C2×#6101—21no—
100C2×#6101—21no—
101C2×#6101D411yescharacteristic
102C2×#6101D411yescharacteristic
103C2×C4×Dic13—21no—
104C2×C4×Dic13—21no—
105C2×C4×Dic13—21no—
106C2×C4×Dic13C2311yescharacteristic
107C2×C4×Dic13C2311yescharacteristic
108C22×#1055C2311yescharacteristic
109C22×#1055C2311yescharacteristic
110#88144—22no—
111#88144C2×C414yes—
112#88142—22no—
113#88142C2×C414yes—
114#88141—44no—
115#88132—28no—
116#88132—28no—
117#88124—22no—
118#88124C2×C414yes—
119C4×Dic26C2×C414yes—
120C4×Dic26D414yes—
121C13×C4⋊C8—22no—
122C13×#102—22no—
123C13×#102—22no—
124#88072—22no—
125#88072Q814yescomplemented
126#88071—21no—
127#88071—21no—
128#88071—21no—
129#88055—22no—
130#88054—22no—
131#88054—22no—
132C8×Dic13—22no—
133#88043—22no—
134#22522—131nomaximal, Sylow
135C24×C13—21no—
136C2×D4×C13—21no—
137C2×D4×C13—21no—
138C2×D4×C13—21no—
139C2×D4×C13C22×C412yes—
140C2×D4×C13C2×Q812yes—
141C2×D4×C13#4112yes—
142C22×C4×C13—21no—
143C22×C4×C13—24no—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13—81no—
147C22×C4×C13—81no—
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2411yescharacteristic
151C22×Dic13—21no—
152C22×Dic13—21no—
153C22×Dic13—21no—
154C22×Dic13—24no—
155C22×Dic13—24no—
156C22×Dic13—21no—
157C22×Dic13—42no—
158C22×Dic13—42no—
159C22×Dic13—81no—
160C22×Dic13—81no—
161C22×Dic13C2×D411yescharacteristic
162C22×Dic13C2×D411yescharacteristic
163C22×Dic13C2×D411yescharacteristic
164C22×Dic13C2×D411yescharacteristic
165C2×Dic26—22no—
166C2×Dic26—22no—
167C2×Dic26—24no—
168C2×Dic26—81no—
169C2×Dic26—81no—
170C2×Dic26C22⋊C414yes—
171C2×C8×C13—21no—
172C2×C8×C13—21no—
173C2×C8×C13—21no—
174C2×C8×C13—21no—
175C2×C8×C13—21no—
176C2×C8×C13—21no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4—21no—
179C13×C4⋊C4—21no—
180C13×C4⋊C4—21no—
181C13×C4⋊C4—21no—
182C13×C4⋊C4—42no—
183C13×C4⋊C4—81no—
184C13×C4⋊C4C22×C412yes—
185C13×C22⋊C4—24no—
186C42×C13C22×C412yes—
187C42×C13C2×D412yes—
188C22⋊Dic13—24no—
189C22⋊Dic13—24no—
190C4⋊Dic13—21no—
191C4⋊Dic13—21no—
192C4⋊Dic13—21no—
193C4⋊Dic13—24no—
194C4⋊Dic13—21no—
195C4⋊Dic13—21no—
196C4⋊Dic13C22⋊C414yes—
197C4⋊Dic13C22×C412yes—
198C4⋊Dic13C22×C412yes—
199C4⋊Dic13C2×Q812yes—
200#6101—24no—
201#6101—24no—
202#6101—24no—
203#6101—24no—
204#6101—42no—
205#6101—42no—
206#6101—81no—
207#6101—81no—
208#6101C22⋊C414yes—
209#6101C22⋊C414yes—
210C4×Dic13—42no—
211C4×Dic13—42no—
212C4×Dic13—42no—
213C4×Dic13C22×C412yes—
214C4×Dic13C22×C412yes—
215C4×Dic13C2×D412yes—
216C4×Dic13C2×D412yes—
217C2×#1055—21no—
218C2×#1055—21no—
219C2×#1055—21no—
220C2×#1055—21no—
221C2×#1055—21no—
222C2×#1055C2×Q812yes—
223C2×#554—131no—
224C2×#446—131no—
225Q8×C4⋊C4—131no—
226#1992—131no—
227#1992—131no—
228#1990—131no—
229#1989—131no—
230#1989—131no—
231#1987—131no—
232#1802—131no—
233#1802—131no—
234#1802D1311yescharacteristic
235#1762—131no—
236#1762—131no—
237C4×#102—131no—
238C23×C13—22no—
239C23×C13—22no—
240C23×C13—22no—
241C23×C13—41no—
242C23×C13—41no—
243C23×C13—41no—
244C23×C13—41no—
245C23×C13C22×D411yescharacteristic
246D4×C13—22no—
247D4×C13—22no—
248D4×C13—22no—
249D4×C13C4×Q814yescomplemented
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—21no—
254C2×C4×C13—22no—
255C2×C4×C13—41no—
256C2×C4×C13—41no—
257C2×C4×C13—41no—
258C2×C4×C13—41no—
259C2×C4×C13—41no—
260C2×C4×C13—41no—
261C2×C4×C13—41no—
262C2×C4×C13—41no—
263C2×C4×C13—84no—
264C2×C4×C13C2×C22⋊C412yes—
265C2×C4×C13C2×C22⋊C412yes—
266C2×C4×C13C23×C411yescharacteristic
267C2×C4×C13C22×D411yescharacteristic
268C2×C4×C13C22×Q811yescharacteristic
269C2×C4×C13C2×#4111yescharacteristic
270C2×C4×C132−1+411yescharacteristic
271C2×C4×C132−1+411yescharacteristic
272C2×Dic13—21no—
273C2×Dic13—21no—
274C2×Dic13—21no—
275C2×Dic13—21no—
276C2×Dic13—21no—
277C2×Dic13—21no—
278C2×Dic13—22no—
279C2×Dic13—22no—
280C2×Dic13—22no—
281C2×Dic13—41no—
282C2×Dic13—41no—
283C2×Dic13—41no—
284C2×Dic13—41no—
285C2×Dic13—41no—
286C2×Dic13—41no—
287C2×Dic13—48no—
288C2×Dic13—41no—
289C2×Dic13—41no—
290C2×Dic13—41no—
291C2×Dic13—84no—
292C2×Dic13C2×C22⋊C412yes—
293C2×Dic13C2×C22⋊C412yes—
294C2×Dic13C2×C22⋊C412yes—
295C2×Dic13C2×C22⋊C412yes—
296C2×Dic13AGL(1,ℤ/8)12yes—
297C2×Dic13#13712yes—
298Dic26—28no—
299Dic26—84no—
300C8×C13—41no—
301C8×C13—41no—
302#1055—22no—
303#1055—41no—
304#554—138no—
305#554—264no—
306C2×C4⋊Q8—131no—
307C2×#125—131no—
308C2×#125—131no—
309C2×C22⋊Q8—261no—
310C2×C22⋊Q8—261no—
311C2×C22⋊Q8—261no—
312C2×C4×Q8—131no—
313C2×C4×Q8—261no—
314C2×C4×D4—131no—
315C2×C4×D4—131no—
316C2×C4×D4C2×D1311yescharacteristic
317C22×C4⋊C4—261no—
318#446—264no—
319C2×C4⋊C8—131no—
320C2×C4⋊C8—131no—
321C2×C4⋊C8C2×D1311yescharacteristic
322C2×#102—131no—
323C2×#102—131no—
324C2×#102C2×D1311yescharacteristic
325C2×#102C2×D1311yescharacteristic
326C2×#97—131no—
327C2×#97—131no—
328C2×C4×C8—131no—
329#389—261no—
330#389—261no—
331#389—261no—
332#384—131no—
333#384—131no—
334#384C2×D1311yescharacteristic
335C4×C4⋊C4—131no—
336C4×C4⋊C4—131no—
337C4×C4⋊C4—131no—
338#340—131no—
339#340—131no—
340#340—131no—
341#340—131no—
342#340—131no—
343#340—131no—
344#340—131no—
345#340—131no—
346#340—131no—
347#340—131no—
348#340C2×D1311yescharacteristic
349#340C2×D1311yescharacteristic
350C22×C13—24no—
351C22×C13—42no—
352C22×C13—42no—
353C22×C13—42no—
354C22×C13—42no—
355C22×C13—42no—
356C22×C13—42no—
357C22×C13C22×C22⋊C411yescharacteristic
358C22×C13#54811yescharacteristic
359C22×C13D4×Q811yescharacteristic
360C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
361C22×C13C2×#13711yescharacteristic
362C22×C13#57611yescharacteristic
363C22×C13#57711yescharacteristic
364C4×C13—22no—
365C4×C13—22no—
366C4×C13—42no—
367C4×C13—81no—
368C4×C13—81no—
369C4×C13C2×C4×Q811yescharacteristic
370C4×C13#51911yescharacteristic
371C4×C13#54811yescharacteristic
372C4×C13D4×Q811yescharacteristic
373Dic13—22no—
374Dic13—22no—
375Dic13—22no—
376Dic13—42no—
377Dic13—42no—
378Dic13—42no—
379Dic13—81no—
380Dic13#41714yes—
381C22×Q8—131no—
382C22×Q8—261no—
383C22×D4C22×D1311yescharacteristic
384C23×C4—21no—
385C23×C4—261no—
386C23×C4—261no—
387C22×C8—131no—
388C22×C8—131no—
389C22×C8C22×D1311yescharacteristic
390C22×C8C22×D1311yescharacteristic
391C4⋊Q8—134no—
392C4⋊Q8—262no—
393#125—134no—
394#125—134no—
395#125—262no—
396#125—262no—
397C22⋊Q8—268no—
398C22⋊Q8—268no—
399C22⋊Q8—268no—
400C4×Q8—134no—
401C4×Q8—134no—
402C4×Q8—524no—
403C4×D4—22no—
404C4×D4—134no—
405C4×D4—134no—
406C4×D4—262no—
407C4×D4—262no—
408C4×D4C4×D1314yes—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—131no—
412C2×C4⋊C4—131no—
413C2×C4⋊C4—131no—
414C2×C4⋊C4—131no—
415C2×C4⋊C4—131no—
416C2×C4⋊C4—131no—
417C2×C4⋊C4—131no—
418C2×C4⋊C4—268no—
419C2×C4⋊C4—261no—
420C2×C4⋊C4—261no—
421C2×C4⋊C4—261no—
422C2×C4⋊C4—261no—
423C2×C4⋊C4—261no—
424C2×C4⋊C4—261no—
425C2×C4⋊C4—261no—
426C2×C4⋊C4—261no—
427C2×C4⋊C4—261no—
428C2×C4⋊C4C22×D1311yescharacteristic
429C2×C4⋊C4C22×D1311yescharacteristic
430C2×C4⋊C4C22×D1311yescharacteristic
431C2×C22⋊C4—21no—
432C2×C22⋊C4—261no—
433C2×C22⋊C4—261no—
434C2×C42—131no—
435C2×C42—131no—
436C2×C42—261no—
437C2×C42—261no—
438C2×C42—261no—
439C2×C42C22×D1311yescharacteristic
440C4⋊C8—22no—
441C4⋊C8—262no—
442C4⋊C8—262no—
443#102—22no—
444#102—22no—
445#102—134no—
446#102—262no—
447#97—262no—
448#97—262no—
449C4×C8—262no—
450#95—261no—
451#95—261no—
452#95—261no—
453C2×C13—44no—
454C2×C13Q8×C22⋊C411yescharacteristic
455C2×C13C2×#41711yescharacteristic
456C2×C13#289711yescharacteristic
457C2×C13#336611yescharacteristic
458C2×C13#337211yescharacteristic
459C2×C13#338411yescharacteristic
460C2×C13#338511yescharacteristic
461C24—21no—
462C2×Q8—134no—
463C2×Q8—262no—
464C2×Q8—262no—
465C2×Q8—264no—
466C2×Q8—1041no—
467C2×Q8—1041no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4C2×C4×D1312yes—
472C2×D4#612912yes—
473C2×D4Q8×D1312yes—
474C22×C4—21no—
475C22×C4—24no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—81no—
479C22×C4—81no—
480C22×C4—131no—
481C22×C4—131no—
482C22×C4—131no—
483C22×C4—131no—
484C22×C4—264no—
485C22×C4—264no—
486C22×C4—261no—
487C22×C4—261no—
488C22×C4—261no—
489C22×C4—261no—
490C22×C4—522no—
491C22×C4—522no—
492C22×C4—1041no—
493C22×C4—1041no—
494C22×C4D4×D1311yescharacteristic
495C22×C4D4×D1311yescharacteristic
496C22×C4C23×D1311yescharacteristic
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—132no—
504C2×C8—261no—
505C2×C8—261no—
506C2×C8—261no—
507C2×C8—261no—
508C2×C8—261no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—42no—
515C4⋊C4—81no—
516C4⋊C4—134no—
517C4⋊C4—134no—
518C4⋊C4—134no—
519C4⋊C4—132no—
520C4⋊C4—132no—
521C4⋊C4—132no—
522C4⋊C4—264no—
523C4⋊C4—264no—
524C4⋊C4—264no—
525C4⋊C4—264no—
526C4⋊C4—264no—
527C4⋊C4—261no—
528C4⋊C4—261no—
529C4⋊C4—261no—
530C4⋊C4—261no—
531C4⋊C4—261no—
532C4⋊C4—522no—
533C4⋊C4—522no—
534C4⋊C4—1041no—
535C4⋊C4—1041no—
536C4⋊C4C2×C4×D1312yes—
537C22⋊C4—24no—
538C22⋊C4—264no—
539C22⋊C4—264no—
540C42—132no—
541C42—132no—
542C42—132no—
543C42—132no—
544C42—522no—
545C42—522no—
546C42—522no—
547C42C2×C4×D1312yes—
548C42D4×D1312yes—
549C13#2252211yescharacteristic, complemented, Sylow
550C23—22no—
551C23—22no—
552C23—22no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23C2×D4×D1311yescharacteristic
558Q8—268no—
559Q8—1044no—
560D4—22no—
561D4—22no—
562D4—22no—
563D4#8814114yescomplemented
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—84no—
578C2×C4—132no—
579C2×C4—132no—
580C2×C4—132no—
581C2×C4—132no—
582C2×C4—132no—
583C2×C4—132no—
584C2×C4—261no—
585C2×C4—261no—
586C2×C4—261no—
587C2×C4—261no—
588C2×C4—261no—
589C2×C4—261no—
590C2×C4—262no—
591C2×C4—262no—
592C2×C4—262no—
593C2×C4—528no—
594C2×C4—521no—
595C2×C4—521no—
596C2×C4—521no—
597C2×C4—521no—
598C2×C4—521no—
599C2×C4—521no—
600C2×C4—521no—
601C2×C4—521no—
602C2×C4—521no—
603C2×C4—1044no—
604C2×C4C22⋊C4×D1312yes—
605C2×C4C22⋊C4×D1312yes—
606C2×C4C22×C4×D1311yescharacteristic
607C2×C4C2×D4×D1311yescharacteristic
608C2×C4C2×#612911yescharacteristic
609C2×C4C2×Q8×D1311yescharacteristic
610C2×C4#8825711yescharacteristic
611C2×C4#8825711yescharacteristic
612C8—41no—
613C8—41no—
614C8—262no—
615C8—521no—
616C22—24no—
617C22—42no—
618C22—42no—
619C22—42no—
620C22—42no—
621C22—42no—
622C22—42no—
623C22C2×C22⋊C4×D1311yescharacteristic
624C22#1171930311yescharacteristic
625C22#1171933711yescharacteristic
626C22#1171946211yescharacteristic
627C22#1171946711yescharacteristic
628C22D13×AGL(1,ℤ/8)11yescharacteristic
629C22D13×#13711yescharacteristic
630C4—22no—
631C4—22no—
632C4—42no—
633C4—81no—
634C4—81no—
635C4—134no—
636C4—262no—
637C4—262no—
638C4—262no—
639C4—522no—
640C4—522no—
641C4—522no—
642C4—1041no—
643C4C2×#8814111yescharacteristic
644C4#1171922111yescharacteristic
645C4#1171930311yescharacteristic
646C4#1171933711yescharacteristic
647C2—44no—
648C2#1311766811yescharacteristic
649C2D13×#41711yescharacteristic
650C2#1312335711yescharacteristic
651C2#1312753811yescharacteristic
652C2#1312761211yescharacteristic
653C2#1312773011yescharacteristic
654C2#1312774111yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1802C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
cosocleC22×C4×C13C24
hypercenter#1802D13
hypocenterC13#22522
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1802

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#11718489C2semidirect
3. #13117748C2semidirect
4. #13115804C2semidirect
5. #13115803C2semidirect
6. #13115795C2semidirect
7. #13115792C2semidirect
8. #13115791C2semidirect
9. #13115782C2semidirect
22. #11719244C4semidirect
125. #88072Q8semidirect
249. D4×C13C4×Q8semidirect
549. C13#22522semidirect
563. D4#88141semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#117192442
C2×#117184892
#131177482
#131158042
#131158032
#131157952
#131157922
#131157912
#131157822
#131148342
#131146632
#131146612
#102×Dic132
C13×#18022
#2252213